Metaplastic and energy-efficient biocompatible graphene artificial synaptic transistors for enhanced accuracy neuromorphic computing

CMOS-based computing systems that employ the von Neumann architecture are relatively limited when it comes to parallel data storage and processing. In contrast, the human brain is a living computational signal processing unit that operates with extreme parallelism and energy efficiency. Although numerous neuromorphic electronic devices have emerged in the last decade, most of them are rigid or contain materials that are toxic to biological systems. In this work, we report on biocompatible bilayer graphene-based artificial synaptic transistors (BLAST) capable of mimicking synaptic behavior. The BLAST devices leverage a dry ion-selective membrane, enabling long-term potentiation, with ~50 aJ/µm2 switching energy efficiency, at least an order of magnitude lower than previous reports on two-dimensional material-based artificial synapses. The devices show unique metaplasticity, a useful feature for generalizable deep neural networks, and we demonstrate that metaplastic BLASTs outperform ideal linear synapses in classic image classification tasks. With switching energy well below the 1 fJ energy estimated per biological synapse, the proposed devices are powerful candidates for bio-interfaced online learning, bridging the gap between artificial and biological neural networks.


Supplementary
. Comparing performance of our BLAST devices to other organic and 2D-material based neuromorphic systems. EC -electrochemical; ++ means high; + moderate;low; * -means material is potentially toxic; N/R -not reported.

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Supplementary Note 1. Nonlinearity, read noise, and write noise calculation To calculate nonlinearity, following the methodology outlined in Reference 29 , the averaged ramp is normalized and a fitting is calculated for the following equations: where ! and ( are the ramp values for potentiation and depression, %)* and %&' are the maximum and minimum conductance, and %)* is the maximum pulse number for the ramp. The fitting parameter describes the nonlinearity of the ramp, where = 0 is perfect linearity.
Write noise is calculated using the standard deviation of the averaged ramp, which is in turn averaged across all pulses: where is a conductance sample, ̅ is the mean of the samples, and is the number of samples.
Read noise is calculated by first grouping all sampled data by conductance level and calculating the standard deviation as follows: where is a conductance sample, ̅ is the mean of the samples, and is the number of samples.
The average read noise across the dynamic range of the device is then calculated:

Supplementary Note 2. Energy dissipation per update calculation
Gate current and voltage are monitored for a current spike and the channel conductance before, during, and after the update are recorded. The raw energy dissipation can be obtained using: where < and < are gate current and voltage respectively, and A and B denote the time window of the measurement.
To make the calculation generalizable across devices with different channel area, normalization is done according to device area: where DE)''/-is the device channel area. In order to make sure that the value represents a similar change in conductance across all devices, a linear scaling law is assumed to scale all energy values to the energy required to change the conductance of the device by 1%, chosen since it is close to the write noise of the devices: where %)* and %&' are the maximum and minimum channel conductances.

Supplementary Note 3. Read power dissipation
The read operation of the device depends on the channel conductance. As a result, the energy required for a read operation can be described as follows: where 7/)@ is the read power, 7/)@ is the applied read voltage, is the channel conductance, and 7/)@ is the read pulse length.  Table S1.

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Supplementary Figure 13. a, mBLAST performance at various temperatures for b, average change in conductance, c, write noise, d, normalized conductance range, and e, linearity. There is a clear change in performance between 40°C and 60°C in all metrics evaluated.
Supplementary Figure 14. mBLAST performance at various read voltage (J for a, conductance, b, pulse sweeps, c, nonlinearity, and d, write noise. There is some variability in performance for all presented metrics at voltages below 50 mV which stabilizes above 50 mV. This is most likely due to the read noise at low voltage. Supplementary Figure 16. Learning rate sweep confirming that the training benefit for µBLAST synapses is not limited to specific learning rates. Supplementary Figure 17. Graphical representation of the modified update scheme for the numerical metaplastic weights. The computed optimizer update is multiplied by β, emulating the synaptic characteristics of µBLASTs. β for the positive (negative) update is shown in blue (red).
Supplementary Figure 18. Histogram representation of weight distributions for a, b, numeric uniform, c, d, µBLASTs, and e, f, numeric metaplastic, for the 1 st and 2 nd layer, respectively. The shape of the weight distribution for µBLASTs qualitatively matches that of the numeric metaplastic weights, confirming a weight normalization effect.